C-Integrability Test for Discrete Equations via Multiple Scale Expansions
In this paper, we are extending the well-known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example, we apply the theory to the case of a differential-difference dispersive equation of the Burgers hierarchy which via a discrete...
Збережено в:
| Дата: | 2010 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146506 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | C-Integrability Test for Discrete Equations via Multiple Scale Expansions / C. Scimiterna, D. Levi // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146506 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1465062019-02-10T01:24:35Z C-Integrability Test for Discrete Equations via Multiple Scale Expansions Scimiterna, C. Levi, D. In this paper, we are extending the well-known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example, we apply the theory to the case of a differential-difference dispersive equation of the Burgers hierarchy which via a discrete Hopf-Cole transformation reduces to a linear differential-difference equation. In this case, the equation satisfies the A₁, A₂ and A₃ linearizability conditions. We then consider its discretization. To get a dispersive equation we substitute the time derivative by its symmetric discretization. When we apply to this nonlinear partial difference equation the multiple scale expansion we find out that the lowest order non-secularity condition is given by a non-integrable nonlinear Schrödinger equation. Thus showing that this discretized Burgers equation is neither linearizable not integrable. 2010 Article C-Integrability Test for Discrete Equations via Multiple Scale Expansions / C. Scimiterna, D. Levi // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34K99; 34E13; 37K10; 37J30 DOI:10.3842/SIGMA.2010.070 http://dspace.nbuv.gov.ua/handle/123456789/146506 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In this paper, we are extending the well-known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example, we apply the theory to the case of a differential-difference dispersive equation of the Burgers hierarchy which via a discrete Hopf-Cole transformation reduces to a linear differential-difference equation. In this case, the equation satisfies the A₁, A₂ and A₃ linearizability conditions. We then consider its discretization. To get a dispersive equation we substitute the time derivative by its symmetric discretization. When we apply to this nonlinear partial difference equation the multiple scale expansion we find out that the lowest order non-secularity condition is given by a non-integrable nonlinear Schrödinger equation. Thus showing that this discretized Burgers equation is neither linearizable not integrable. |
| format |
Article |
| author |
Scimiterna, C. Levi, D. |
| spellingShingle |
Scimiterna, C. Levi, D. C-Integrability Test for Discrete Equations via Multiple Scale Expansions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Scimiterna, C. Levi, D. |
| author_sort |
Scimiterna, C. |
| title |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions |
| title_short |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions |
| title_full |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions |
| title_fullStr |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions |
| title_full_unstemmed |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions |
| title_sort |
c-integrability test for discrete equations via multiple scale expansions |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146506 |
| citation_txt |
C-Integrability Test for Discrete Equations via Multiple Scale Expansions / C. Scimiterna, D. Levi // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT scimiternac cintegrabilitytestfordiscreteequationsviamultiplescaleexpansions AT levid cintegrabilitytestfordiscreteequationsviamultiplescaleexpansions |
| first_indexed |
2023-05-20T17:24:57Z |
| last_indexed |
2023-05-20T17:24:57Z |
| _version_ |
1796153237697462272 |